Re: Concurrency in an RDB - another question about recursive definitions
From: paul c <toledobythesea_at_oohay.ac>
Date: Sat, 20 Jan 2007 19:52:46 GMT
Message-ID: <iqush.728297$5R2.588249_at_pd7urf3no>
>> paul c wrote:
>>
>>> Bob Badour wrote:
>>>
>>>> paul c wrote:
>>>>
>>>>> Bob Badour wrote:
>>>>>
>>>>>> ...
>>>>>> What I am saying is: When you project onto A, the data type of B
>>>>>> is mostly** irrelevant. Likewise, when you project onto B, the
>>>>>> data type of A is mostly irrelevant.
>>>>>>
>>>>>> The fact that you have a recursive data type definition has no
>>>>>> effect on project or join or restrict or union or intersect or
>>>>>> difference etc. The values identified as B are simply values.
>>>>>>
>>>>>> Assuming:
>>>>>>
>>>>>> A = { a1, a2, a3, a4, a5 }
>>>>>> B = { {a,b} | a in A and b in B }
>>>>>>
>>>>>> Given relation R{a in A,b in B}: /* Using C-style comments */
>>>>>>
>>>>>> R = { { a1, { a2, { a3, {} } } } /* a=a1, b={ a2, { a3, {} } */
>>>>>> , { a4, { a3, {} } } /* a=a4, b={ a3, {} } */
>>>>>> , { a5, { a2, { a3, {} } } } /* a=a5, b={ a2, { a3, {} } */
>>>>>> }
>>>>>> ...
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>> Bob, now I remember a parallel question that struck me about your
>>>>> subtle definition of B, B = { {a,b} | a in A and b in B }. I take
>>>>> it that you meant B to be a type that is used by the R relation.
>>>>> But is it somehow plausible to see B as a relation?
>>>>
>>>>
>>>>
>>>>
>>>>
>>>> B must be a relation type, in fact.
>>>>
>>>>
>>>>> If so, I would think that a value for relation B that has one tuple:
>>>>>
>>>>> B = { { a1, {a2, {a3, {} } } } } /* a=a1, b={ a2, { a3, {} } */
>>>>>
>>>>> is not possible because by definition (B "referencing" itself),
>>>>> there would need to be two additional tuples to make it stick to
>>>>> the definition, namely
>>>>>
>>>>> { a2, { a3, {} }
>>>>>
>>>>> and
>>>>>
>>>>> { a3, {} }.
>>>>>
>>>>> Thanks for any comments,
>>>>> p
>>>>
>>>>
>>>>
>>>>
>>>>
>>>> Relations are sets and {} is one of them. Thus {} is a valid B
>>>> value; although, I omitted the headers for brevity. Joe Thurbon
>>>> introduced a ...
>>>
>>>
>>>
>>>
>>> Thanks but if this is answering my question, it may be too terse for
>>> me to see it!
>>>
>>> Are you saying that
>>>
>>> B = { { a1, {a2, {a3, {} } } } } /* a=a1, b={ a2, { a3, {} } */
>>>
>>> is possible, given the self-refencing definition?
>>> p
>>
>>
>>
>> Let me change that last comment to:
>>
>> (Whereas I was thinking that it would be impossible for B to have only
>> one such tuple.)
Date: Sat, 20 Jan 2007 19:52:46 GMT
Message-ID: <iqush.728297$5R2.588249_at_pd7urf3no>
Bob Badour wrote:
> paul c wrote: >
>> paul c wrote:
>>
>>> Bob Badour wrote:
>>>
>>>> paul c wrote:
>>>>
>>>>> Bob Badour wrote:
>>>>>
>>>>>> ...
>>>>>> What I am saying is: When you project onto A, the data type of B
>>>>>> is mostly** irrelevant. Likewise, when you project onto B, the
>>>>>> data type of A is mostly irrelevant.
>>>>>>
>>>>>> The fact that you have a recursive data type definition has no
>>>>>> effect on project or join or restrict or union or intersect or
>>>>>> difference etc. The values identified as B are simply values.
>>>>>>
>>>>>> Assuming:
>>>>>>
>>>>>> A = { a1, a2, a3, a4, a5 }
>>>>>> B = { {a,b} | a in A and b in B }
>>>>>>
>>>>>> Given relation R{a in A,b in B}: /* Using C-style comments */
>>>>>>
>>>>>> R = { { a1, { a2, { a3, {} } } } /* a=a1, b={ a2, { a3, {} } */
>>>>>> , { a4, { a3, {} } } /* a=a4, b={ a3, {} } */
>>>>>> , { a5, { a2, { a3, {} } } } /* a=a5, b={ a2, { a3, {} } */
>>>>>> }
>>>>>> ...
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>> Bob, now I remember a parallel question that struck me about your
>>>>> subtle definition of B, B = { {a,b} | a in A and b in B }. I take
>>>>> it that you meant B to be a type that is used by the R relation.
>>>>> But is it somehow plausible to see B as a relation?
>>>>
>>>>
>>>>
>>>>
>>>>
>>>> B must be a relation type, in fact.
>>>>
>>>>
>>>>> If so, I would think that a value for relation B that has one tuple:
>>>>>
>>>>> B = { { a1, {a2, {a3, {} } } } } /* a=a1, b={ a2, { a3, {} } */
>>>>>
>>>>> is not possible because by definition (B "referencing" itself),
>>>>> there would need to be two additional tuples to make it stick to
>>>>> the definition, namely
>>>>>
>>>>> { a2, { a3, {} }
>>>>>
>>>>> and
>>>>>
>>>>> { a3, {} }.
>>>>>
>>>>> Thanks for any comments,
>>>>> p
>>>>
>>>>
>>>>
>>>>
>>>>
>>>> Relations are sets and {} is one of them. Thus {} is a valid B
>>>> value; although, I omitted the headers for brevity. Joe Thurbon
>>>> introduced a ...
>>>
>>>
>>>
>>>
>>> Thanks but if this is answering my question, it may be too terse for
>>> me to see it!
>>>
>>> Are you saying that
>>>
>>> B = { { a1, {a2, {a3, {} } } } } /* a=a1, b={ a2, { a3, {} } */
>>>
>>> is possible, given the self-refencing definition?
> > > Yes, it is possible. In fact, the above describes it. > >>>>
>>> (Whereas I was thinking that it would be impossible for B to have
>>> only one tuple.)
>>> p
>>
>>
>>
>> Let me change that last comment to:
>>
>> (Whereas I was thinking that it would be impossible for B to have only
>> one such tuple.)
> > > How so?
I thought by those three words "b in B", part of the "B = { {a,b} | a in A and b in B }" definition. In the "tuple" "/* a=a1, b={ a2, { a3, {} } */" I took there to be several "nested" b values, eg., b={ a3, {} } being one. Would it not need to be "in" B as a tuple in its own right ("unnested", if you will)? Is this fatuous (I won't be offended if it is)?
p Received on Sat Jan 20 2007 - 20:52:46 CET